<p>
  By fixing the maturity and looking at the implied volatilities of European options on the same underlying but different strikes, we obtain the implied volatility skew or smile. The volatility surface is the three-dimensional surface when we plots the market implied volatilities of European options with different strikes and different maturities.
</p>
<p>
  Through the interpolation method, we can generate the implied volatility surface of SPY options for both put and call options as follows:
</p>
<img class="img-responsive" src="https://cdn.quantconnect.com/tutorials/i/Tutorial06-vol-surface-call.png" alt="implied volatility surface for call options"/>
<img class="img-responsive" src="https://cdn.quantconnect.com/tutorials/i/Tutorial06-vol-surface-put.png" alt="implied volatility surface for put options"/>
